In the intro, it does not mention Korra by name, it just says 'the last avatar', you just assumed, and they don't say it was recently, just that they were still reeling from her loss. That implies recently, but based on the lore of the show, it cannot be more recently than our character's birth. Recent is relative after all, and in this case, was likely 15-20 years ago, or however old you are supposed to be.
If he did mean that he became the avatar as a teen, then that is a mistake, since that is not how the lore of the show works.
Shortly after that, in the intro, they talk about him being fire nation, and he pretends that he can bend, when talking to the painted lady.
He says,
"I definitely know how to do some stuff. What do you need? Firebending? I can totally do that. Yup, definitely not lying."
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Not to mention how much more advanced their tech levels are then in the show...